Epistasis could be an important source of risk for disease. How interacting loci might be discovered is an open question for genome-wide association studies (GWAS). Most researchers limit their statistical analyses to testing individual pairwise interactions (i.e., marginal tests for association). A more effective means of identifying important predictors is to fit models that include many predictors simultaneously (i.e., higher-dimensional models). We explore a procedure called screen and clean (SC) for identifying liability loci, including interactions, by using the lasso procedure, which is a model selection tool for high-dimensional regression. We approach the problem by using a varying dictionary consisting of terms to include in the model. In the first step the lasso dictionary includes only main effects. The most promising single-nucleotide polymorphisms (SNPs) are identified using a screening procedure. Next the lasso dictionary is adjusted to include these main effects and the corresponding interaction terms. Again, promising terms are identified using lasso screening. Then significant terms are identified through the cleaning process. Implementation of SC for GWAS requires algorithms to explore the complex model space induced by the many SNPs genotyped and their interactions. We propose and explore a set of algorithms and find that SC successfully controls Type I error while yielding good power to identify risk loci and their interactions. When the method is applied to data obtained from the Wellcome Trust Case Control Consortium study of Type 1 Diabetes it uncovers evidence supporting interaction within the HLA class II region as well as within Chromosome 12q24. Genet. Epidemiol. 34: 275–285, 2010. © 2010 Wiley-Liss, Inc.